Very spare, simple, unpretentious prose. There are no complex ideas and it's tied up a bit too tidy by the end, but on the whole I liked it as it remiVery spare, simple, unpretentious prose. There are no complex ideas and it's tied up a bit too tidy by the end, but on the whole I liked it as it reminded me of my own explorations into the woods as a child, as well as the lost childhood friendships that slowly fade to nothing.
A very good intro book for abstract algebra. It's short and sweet, but according to people who know more about the subject than I do, it has everythinA very good intro book for abstract algebra. It's short and sweet, but according to people who know more about the subject than I do, it has everything you should get in a first course. The style is conversational with lots of examples, but is not overly wordy. The theorems stand out visually from the page enough to find them, and a good amount of details are omitted as exercises. The problems are a good mix of difficulty. Comparing it to Lang I see now that they are a bit on the easy side, but still time-consuming and non-trivial, especially the later ones in the set. Almost all are proof-based....more
I picked up this book to fill in a hole in my math education in preparation for the GRE math subject test, and because it was far and away the cheapesI picked up this book to fill in a hole in my math education in preparation for the GRE math subject test, and because it was far and away the cheapest abstract algebra book I could find. I'm not particularly thrilled with it yet; it's better than an elementary approach I borrowed but I may just keep looking.
First, the text is a bit dated. It a corrected version of the 1966 printing. Some of the notation is not what is currently standard, which is a little inconvenient: "J" for the integers instead of "Z" (and without the mathbb font), etc. More irksome is the typography: the breaks between examples, lemmas, theorems, etc. are indistinguishable from equation line breaks, and so it's difficult to return to the statement of a theorem to verify something, or to notice at a glance where one one idea ends and another begins. The text is not overly cluttered with diagrams and simplistic explanations, which I like, but in areas such as Diophantine equations I feel it might benefit from a less dense approach. Theorems introduce 8 or 9 quantities by variable name only; even a bold typeface or subscripts or something might help certain subsets of variables stand apart from others in these cases.
The upside is that the text is pretty rigorous, and builds number systems and operations axiomatically all from the natural numbers. For someone who is already familiar with the properties of integers, the reals, etc., this is an interesting approach. The construction of the integers in particular was a new one for me....more
This is a concise, clear, well-researched and nuanced indictment of the legislative branch of the U.S. government. Lessig describes how the governmentThis is a concise, clear, well-researched and nuanced indictment of the legislative branch of the U.S. government. Lessig describes how the government has become dependent on special interest money, allowing big business to dictate policy, write special exemption into tax law, and generally strangle healthy free market competition. All the while government gets more bloated and incapable of solving problems. This systemic corruption is a far cry from the dramatic tit-for-tat bribery and swindling that occasionally makes headlines.
Because the corruption Lessig describes is less visible and less tangible, it's not as easy to build a movement against it. It's the same reason more people get up in arms against terrorism than pollution, or heart disease. One is a better story than the other. Yet this really should be the #1 issue of both the political left and right, because, while there are real issues that divide us, there are also plenty of non-issues that have widespread support but never get implemented, because of the stranglehold money has on our system. Big Business and Big Government in bed together.
Very thought-provoking. I began this book resistant to its message, as I had watched speeches by Dennett that had left me unconvinced. Specifically IVery thought-provoking. I began this book resistant to its message, as I had watched speeches by Dennett that had left me unconvinced. Specifically I had taken away from those presentations that to Dennett consciousness, or "mindhood", was nothing more than a byproduct of the organization of the brain, which, while potentially true, was dismissive of the subjectiveness of being, something separated from objective analysis by (to me) an unbridgeable chasm. I've heard it facetiously argued that perhaps those who utterly dismiss subjectivity and "qualia" themselves have no minds -- they are walking philosophical zombies.
Well the charge is false with Dennett, because he devotes a whole chapter to such concerns in this book. The contemptuousness held toward the subjective was entirely imagined on my part. Still, while I can agree that consciousness might be nothing more than a principle of organization, no amount of puzzling over it has ever allowed me to intuit such a result.
The main premise of Kinds of Minds is that, instead of an arbitrary cutoff between conscious and unconscious creatures, there is a fuzzy gradation, with the fundamental kinds of consciousness changing along the way. What's more surprising is the way he uses current science to actually flesh out reasonable guesses as to what some of of these kinds of consciousness might look like. He uses the same experiments and thought experiments to propose that human consciousness might be further removed from the animal kind than we tend to think, and that language is the key innovation that has endowed us with conceptual consciousness.
It's clear to me that my own tendency has been to extend the envelope of consciousness to a broader host of organisms than most people do. But when I think about it now I will be reminding myself that other animals are not just Humanity, Lite, but qualitatively different, in a way that may be difficult or impossible to imagine in anything other than a stretched analogy.
I read this because I very much like such imaginings, and I was not disappointed....more